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We consider two equivariant equations admitting s v u c t d l y stable heteroclinic cycles. These equations stem from mode equations for the Rayleigh-Benard convection and a model for turbulent layen in wall rrgions with riblets. Breaking'the symmetry causes several different bifurcations to occur which a n be explained by bifurcations of codimension two of homoclinic orbits for non-symmetric syitems. In particular, stable periodic solutions of different symmetry type. other complicateddoi:10.1088/0951-7715/8/3/003 fatcat:rcr67psxljdy5foiay6noesspy